Finite Group Databasebeta

← #22625885

Subgroups — #22625885

Order 9344.

278 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D73⋊M16C211yesmaximal, characteristic
2C2×#14556662C211yesmaximal, characteristic, complemented
3C2×#14556661C211yesmaximal, characteristic, complemented
4#17989558C211yesmaximal, characteristic
5#17989463C211yesmaximal, characteristic, complemented
6#17989463C211yesmaximal, characteristic, complemented
7C22⋊C8×D73C211yesmaximal, characteristic
8C2×#11924038C2211yescharacteristic
9C2×#11924038C2211yescharacteristic
10C2×#11924038C2211yescharacteristic
11C2×#11924038C2211yescharacteristic
12D73⋊M16—22no—
13D73⋊M16—22no—
14C2×#11924037—21no—
15C2×#11924036—21no—
16#14556662—22no—
17#14556661—22no—
18#14556648—21no—
19C22⋊#10596833—21no—
20C22×C4×D73C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23C22⋊#10596831C411yescharacteristic
24#14556503C411yescharacteristic
25#14556503C411yescharacteristic
26C22⋊C8×C73C411yescharacteristic
27#11924038—21no—
28#11924038—21no—
29#11924038—21no—
30#11924038—21no—
31#11924038—21no—
32#11924038—21no—
33#11924038D412yes—
34#11924038D412yes—
35#11924037—24no—
36#11924036—24no—
37C2×#10596833—21no—
38C2×#10596833—21no—
39C2×#10596833—21no—
40C2×#10596833—21no—
41C23×D73Q811yescharacteristic
42C22×Dic73D411yescharacteristic
43C2×C4×D73—21no—
44C2×C4×D73—21no—
45C2×C4×D73—21no—
46C2×C4×D73—21no—
47C2×C4×D73C2×C411yescharacteristic
48C2×C4×D73D411yescharacteristic
49C2×C4×D73Q811yescharacteristic
50C2×C4×D73C2311yescharacteristic
51C2×#10596831C2×C411yescharacteristic
52C2×#10596831C2×C411yescharacteristic
53C8×D73—21no—
54C8×D73—21no—
55C8×D73—21no—
56C8×D73—21no—
57C22×C4×C73C2×C411yescharacteristic
58C2×C8×C73C2×C411yescharacteristic
59C2×C8×C73C2×C411yescharacteristic
60C23×C73C4⋊C411yescharacteristic
61C22×D73—22no—
62C22×D73—21no—
63C22×D73—21no—
64C22×D73—41no—
65C22×D73C4⋊C411yescharacteristic
66C22×D73C2×Q811yescharacteristic
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73C4⋊C411yescharacteristic
70C2×C4×C73C22×C411yescharacteristic
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73C4⋊C411yescharacteristic
74C2×Dic73C2×D411yescharacteristic
75C4×D73—21no—
76C4×D73—21no—
77C4×D73—21no—
78C4×D73—21no—
79C4×D73—21no—
80C4×D73—21no—
81C4×D73C2×D411yescharacteristic
82C4×D73C2×D411yescharacteristic
83C4×D73#4111yescharacteristic
84C4×D73#4111yescharacteristic
85#10596833—22no—
86#10596833—22no—
87#10596833—41no—
88#10596833—41no—
89C8×C73—21no—
90C8×C73—21no—
91#10596831—21no—
92#10596831—21no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73—21no—
96C22×C73C2×C4⋊C411yescharacteristic
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—21no—
101C2×D73—42no—
102C2×D73—42no—
103C2×D73#10812yescomplemented
104C2×D73C22⋊Q811yescharacteristic
105C2×D73C22⋊Q811yescharacteristic
106C4×C73—21no—
107C4×C73C4×D411yescharacteristic
108C4×C73C4×D411yescharacteristic
109Dic73—21no—
110Dic73#12011yescharacteristic
111Dic73#12311yescharacteristic
112C2×C73—41no—
113C2×C73#38511yescharacteristic
114C2×C73C2×#10811yescharacteristic
115C2×C73#43011yescharacteristic
116D73—22no—
117D73—21no—
118D73—21no—
119#1855—731nomaximal, Sylow
120C73#185511yescharacteristic, complemented, Sylow
121C22×M16—731no—
122C2×#108—731no—
123C2×#108—731no—
124#407—731no—
125C2×C22⋊C8—731no—
126#341—731no—
127#341—731no—
128C23×C4—731no—
129C2×M16—731no—
130C2×M16—731no—
131C2×M16—731no—
132C2×M16—731no—
133C2×M16—1462no—
134C2×M16—1462no—
135C2×M16—1461no—
136C22×C8—731no—
137C22×C8—731no—
138C22×C8—1461no—
139#108—1462no—
140#108—1462no—
141C22⋊C8—731no—
142C22⋊C8—731no—
143C22⋊C8—731no—
144C22⋊C8—1461no—
145C22⋊C8—1461no—
146C22⋊C8#6440811yescharacteristic
147C24—731no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—1461no—
154C22×C4—1461no—
155C22×C4—1461no—
156C22×C4—1461no—
157C22×C4C2×#6440811yescharacteristic
158M16—732no—
159M16—732no—
160M16—1461no—
161M16—1461no—
162M16—1461no—
163M16—1461no—
164M16—1461no—
165M16—1461no—
166M16—1464no—
167C2×C8—731no—
168C2×C8—731no—
169C2×C8—1461no—
170C2×C8—1461no—
171C2×C8—1461no—
172C2×C8—1461no—
173C2×C8—1461no—
174C2×C8—1461no—
175C2×C8—1461no—
176C2×C8—1461no—
177C2×C8—1464no—
178C2×C8C2×#6440811yescharacteristic
179C2×C8C2×#6440811yescharacteristic
180C23—2921no—
181C23—731no—
182C23—731no—
183C23—1461no—
184C23—1461no—
185C23—1462no—
186C23C4⋊#6440811yescharacteristic
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—1461no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4C4⋊#6440811yescharacteristic
204C2×C4C22×#6440811yescharacteristic
205C8—21no—
206C8—21no—
207C8—2921no—
208C8—2921no—
209C8—1462no—
210C8—1462no—
211C8—1461no—
212C8—1461no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—2922no—
217C22—2922no—
218C22—731no—
219C22—731no—
220C22—732no—
221C22—1461no—
222C22—1461no—
223C22—1461no—
224C22—1461no—
225C22C2×C4⋊#6440811yescharacteristic
226C4—21no—
227C4—731no—
228C4—731no—
229C4—1461no—
230C4D4×#6440811yescharacteristic
231C4D4×#6440811yescharacteristic
232C2—41no—
233C2—1461no—
234C2—1461no—
235C2—1462no—
236C2#1798953411yescharacteristic
237C2D73⋊#10811yescharacteristic
238C2#1798960211yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC22⋊C8#64408
hypocenterC73#1855
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14556662C2semidirect
3. C2×#14556661C2semidirect
5. #17989463C2semidirect
6. #17989463C2semidirect
103. C2×D73#108semidirect
120. C73#1855semidirect